Problem: Simplify the following expression: $a = \dfrac{q^2 - 5q + 4}{q - 1} $
First factor the polynomial in the numerator. $ q^2 - 5q + 4 = (q - 1)(q - 4) $ So we can rewrite the expression as: $a = \dfrac{(q - 1)(q - 4)}{q - 1} $ We can divide the numerator and denominator by $(q - 1)$ on condition that $q \neq 1$ Therefore $a = q - 4; q \neq 1$